1. Field of the Invention
The present invention generally relates to the measurement of network parameters with a multiport network analyzer and, more particularly, to a method for correcting reciprocity error in two port network measurements.
2. Description of the Related Art
In designing cables and connecting hardware for use with high frequency signals, it is imperative to understand the electrical characteristics of the components used to link a device or cable under-test with the electronics used to transmit and receive data. All of the possible couplings between connectors and cables can be measured with multiport measurement equipment comprising a network analyzer and a switching network. The key to providing an accurate multiport measurement system is a two port calibration procedure which is used repeatedly on every combination of pairs of ports in the measurement system.
Errors associated with network analyzer measurements can result from either non-ideal conditions in the measurement equipment or from the effects of the mechanical fixtures, such as cables and connectors, which are used to connect a device under test (DUT) to the network analyzer or test bed. A simple way to model this error is to view the test bed and the DUT as an ideal network analyzer cascaded with an error network and followed by the DUT. Such a network representation is illustrated in FIG. 1. The intervening network can then be used to account for the effects introduced by internal switching matrices connecting the various analyzer ports to the mechanical fixtures, as well as other sources of loss and distortion within the analyzer. The network can also be used to account for the effects of the fixtures themselves, which effects may introduce loss, crosstalk, and impedance discontinuities. Thus, the ideal network analyzer measures the cascaded network consisting of the intervening linear network followed by the DUT and obtains the measured S-parameters of the composite intervening network and DUT, here denoted as SM. (See FIG. 1).
During testing, the acquired data which is intended to characterize the DUT is oftentimes corrupted by imperfections in the measuring device. The data must therefore be processed to compensate for known errors when extracting the parameters which describe the DUT, here denoted as SA. An algorithm is used to relate the measured parameters SM to the actual parameters SA. However, because the intervening network in the model is partially internal to the measurement equipment, SA cannot be evaluated separately. The only way to characterize SA, therefore, is to measure various DUTs with known electrical characteristics and extract the appropriate parameters from SM. This process is further complicated when switching networks are involved because each change in the switch settings of the network analyzer results in a change in the intervening network due to differences in the signal routing. Thus, a different intervening network exists for each switch setting of the Network Analyzer, and each network must therefore be separately evaluated to compensate for measurement errors.
In general, the characterization of a two port reciprocal network results in a symmetric 2xc3x972 S-parameter matrix. Measurements of this network should therefore show this symmetry but they are often corrupted by noise, resulting in asymmetrical data. This error, which is denoted as reciprocity error, affects the calculations performed on measured data which are intended to correct measurement error. Specifically, the reciprocity error directly affects the noise floor of the calculation of the scattering between modes of propagation in cables and connecting hardware.
It would therefore be advantageous to provide a method for correcting the reciprocity error in measured data obtained during the characterization of a 2xc3x972 S-parameter matrix.
The above and other problems are overcome by a method for correcting reciprocity error in two port network measurements which is used to produce a matrix with an optimal symmetric approximation of a measured 2xc3x972 reciprocal network. According to the invention, an iterative technique is used to smooth the measured data to obtain a low noise floor on measurements related to mode conversion in cables and connecting hardware.
The calibration procedure for network analyzer measurements relates measured data to actual system parameters. These relationships, combined with the requirement for matrix symmetry, define the explicit form of a reciprocity manifold. The closest point on the manifold surface, occurring when a normal to the surface points directly to the measured data point, is used in defining a reciprocal matrix which can be used to estimate the actual device under test (DUT) parameters. In one embodiment, the closest point to the measured data is determined utilizing a successive approximation technique which includes estimating an initial point on a reciprocity manifold, approximating the manifold as a linear surface, and moving along the surface until the normal points directly at the measured data. The data is then projected onto the reciprocity manifold to produce the next iteration in the process.
The method of the invention supplements and extends a conventional two port calibration algorithm to properly compensate for the reciprocity constraint of passive networks such as cables and connecting hardware.